New analytical and numerical solutions for the fractional differential heat-like equation

Abstract

Many researchers have been interested in the study of differential equations, and they have presented many ways to solve them, including exact, approximate, and numerical methods. This paper presented a new iterative method for solving ordinary differential equations (ODEs). This method is based on the concept of Maclaurin expansion, the algorithm of the method was derived, and the convergence of the method was also studied, in addition to applying the method to solve linear, nonlinear, homogeneous, and nonhomogeneous ordinary differential equations of different orders. In the end, the method effectively solved the equations and the approximate solutions obtained by the new method converged to the exact solution.